Introduction: Elastic and Plastic Behaviour of Materials

Push a spring and let it go: it springs back. Squeeze a lump of putty and let it go: it stays squeezed. Both are solids, both were deformed by a force, and yet they respond in completely opposite ways once the force is removed -- this contrast is the starting point of the whole chapter.

A solid is a collection of atoms or molecules held in roughly fixed positions relative to one another by strong interatomic forces. When an external force is applied to a solid, these atoms are displaced slightly from their normal (equilibrium) positions, and the interatomic forces resist this displacement, setting up an internal restoring force that tries to bring the atoms back. If, once the deforming force is removed, this restoring force succeeds in bringing every atom exactly back to its original position -- so the body regains its original size and shape completely -- the body's behaviour is called elastic, and the property itself is called elasticity. A steel ruler bent gently between two fingers and released, a rubber band stretched and let go, a diving board that flexes under a diver's weight and springs back -- all of these are (nearly) elastic.

If, on the other hand, the body does not return to its original shape, and instead stays in the new, deformed shape even after the force is removed, the body's behaviour is called plastic, and the property is called plasticity. Wet clay, dough, putty, and soft chewing gum are everyday examples: squeeze or stretch them into a new shape, and they simply stay that way.

No real material is perfectly elastic or perfectly plastic in every situation -- these are two ends of a spectrum. Steel, glass, and most metals are very nearly perfectly elastic as long as the deforming force is kept small enough (within what this chapter will call the elastic limit); the same steel, pushed or pulled hard enough, will eventually deform permanently, i.e. behave plastically. This is exactly why an engineer designing a bridge cable, a vehicle spring, or a building's structural steel needs to know not just whether a material is elastic, but how much stress it can safely carry while still remaining elastic -- which is precisely what the stress-strain relationship, developed over the rest of this chapter, is used to answer.

To make "how much a body deforms for a given force" a precise, comparable, material-specific quantity -- rather than something that depends on the exact size and shape of the particular sample being tested -- physics defines two related ideas: stress, the internal force set up per unit area in response to the deforming force, and strain, the fractional deformation produced. The next section defines both precisely, along with the three distinct kinds of deformation (a change in length, a change in shape, and a change in volume) that a solid can undergo.